Question

Difficulty: HardContour Lines and Relief Representation

On a topographical map with a scale of 1:25,0001 : 25,000 and a contour interval of 20 m20\text{ m}, a river flows down a valley. Contour line V1V_1, whose V-shape apex points upstream toward higher elevation, crosses the river channel at an elevation of 360 m360\text{ m}. Further downstream, the river crosses contour line V2V_2, which is separated from V1V_1 by 44 contour intervals. If the measured map distance along the stream between these two crossing points is 8 cm8\text{ cm}, what is the average gradient of the river channel between V1V_1 and V2V_2?

  1. 1 in 25Answer
  2. B
    1 in 2,500
  3. C
    1 in 20
  4. D
    1 in 2.5

Answer

The average gradient of the river channel between points V1 and V2 is 1 in 25.
The vertical interval (VI) represents the height difference between the two points along the stream, which is equal to 4 intervals×20 m=80 m4 \text{ intervals} \times 20\text{ m} = 80\text{ m}. The horizontal equivalent (HE) is calculated by multiplying the map distance (8 cm8\text{ cm}) by the scale factor (25,00025,000), yielding 200,000 cm200,000\text{ cm} or 2,000 m2,000\text{ m}. Dividing VI by HE yields 802000=125\frac{80}{2000} = \frac{1}{25}, expressed as a ratio of 1 in 25.

Step-by-Step Solution

1
Calculate the Vertical Interval (VI) between contour crossings
Vertical Interval (VI) = 4 intervals×20 m=80 m4 \text{ intervals} \times 20\text{ m} = 80\text{ m}
Since the stream flows downstream, elevation drops by 4 contour intervals from the initial elevation of 360m.
2
Convert the map distance to actual ground distance (Horizontal Equivalent, HE)
Ground distance (HE) = 8 cm×25,000=200,000 cm=2,000 m8\text{ cm} \times 25,000 = 200,000\text{ cm} = 2,000\text{ m}
Map scale 1 : 25,000 means 1 cm on the map equals 25,000 cm (or 250 m) on the ground.
3
Calculate the gradient using the ratio formula VI / HE
Gradient = 80 m2,000 m=125\frac{80\text{ m}}{2,000\text{ m}} = \frac{1}{25} or 1 in 251 \text{ in } 25
Both Vertical Interval and Horizontal Equivalent must be expressed in the same unit (meters) to compute the gradient ratio.

Key Concept

Topographic Gradient and Relief Interpretation
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